Computation, Volume 9, Issue 8 (August 2021) – 13 articles

The density functional theory developed earlier for Coulombic excited states is reconsidered using the nodal variational principle. It is much easier to solve the Kohn–Sham equations, because only the correct number of nodes of the orbitals should be insured instead of the orthogonality. Full article

In this paper, we construct novel numerical algorithms to solve the heat or diffusion equation. We start with 10⁵ different leapfrog-hopscotch algorithm combinations and narrow this selection down to five during subsequent tests. We demonstrate the performance of these top five methods in the case of large systems with random parameters and discontinuous initial conditions, by comparing them with other methods. We verify the methods by reproducing an analytical solution using a non-equidistant mesh. Then, we construct a new nontrivial analytical solution containing the Kummer functions for the heat equation with time-dependent coefficients, and also reproduce this solution. The new methods are then applied to the nonlinear Fisher equation. Finally, we analytically prove that the order of accuracy of the methods is two, and present evidence that they are unconditionally stable. Full article

Parameter estimation of complex nonlinear turbulent dynamical systems using only partially observed time series is a challenging topic. The nonlinearity and partial observations often impede using closed analytic formulae to recover the model parameters. In this paper, an exact path-wise sampling method is developed, which is incorporated into a Bayesian Markov chain Monte Carlo (MCMC) algorithm in light of data augmentation to efficiently estimate the parameters in a rich class of nonlinear and non-Gaussian turbulent systems using partial observations. This path-wise sampling method exploits closed analytic formulae to sample the trajectories of the unobserved variables, which avoid the numerical errors in the general sampling approaches and significantly increase the overall parameter estimation efficiency. The unknown parameters and the missing trajectories are estimated in an alternating fashion in an adaptive MCMC iteration algorithm with rapid convergence. It is shown based on the noisy Lorenz 63 model and a stochastically coupled FitzHugh–Nagumo model that the new algorithm is very skillful in estimating the parameters in highly nonlinear turbulent models. The model with the estimated parameters succeeds in recovering the nonlinear and non-Gaussian features of the truth, including capturing the intermittency and extreme events, in both test examples. Full article

In this article, the recently introduced iterative scheme of Hassan et al. (Math. Probl. Eng. 2020) is re-analyzed with the connection of Reich–Suzuki type nonexpansive (RSTN) maps. Under mild conditions, some important weak and strong convergence results in the context of uniformly convex Banach spaces are provided. To support the main outcome of the paper, we provide a numerical example and show that this example properly exceeds the class of Suzuki type nonexpansive (STN) maps. It has been shown that the Hassan et al. iterative scheme of this example is more useful than the many other iterative schemes. We provide an application of our main results to solve split feasibility problems in the setting of RSTN maps. The presented outcome is new and compliments the corresponding results of the current literature. Full article

We study epidemic Susceptible–Infected–Susceptible (SIS) models in the fractional setting. The novelty is to consider models in which the susceptible and infected populations evolve according to different fractional orders. We study a model based on the Caputo derivative, for which we establish existence results of the solutions. Furthermore, we investigate a model based on the Caputo–Fabrizio operator, for which we provide existence of solutions and a study of the equilibria. Both models can be framed in the context of SIS models with time-varying total population, in which the competition between birth and death rates is macroscopically described by the fractional orders of the derivatives. Numerical simulations for both models and a direct numerical comparison are also provided. Full article

In this paper, we consider the task of the analysis, modeling, and application of dependencies between asset quotes at various capital markets. As an example, we study the dependency between financial instrument observation series in the currency and stock markets. Our work intends to give a theoretical basis to asset management strategies that estimate an asset’s price via regression, taking into account its correlated assets in various markets. Furthermore, we provide a way to increase the estimate quality using an evolutionary algorithm. Full article

Interfacial thermal resistance (ITR) plays a critical role in the thermal properties of a variety of material systems. Accurate and reliable ITR prediction is vital in the structure design and thermal management of nanodevices, aircraft, buildings, etc. However, because ITR is affected by dozens of factors, traditional models have difficulty predicting it. To address this high-dimensional problem, we employ machine learning and deep learning algorithms in this work. First, exploratory data analysis and data visualization were performed on the raw data to obtain a comprehensive picture of the objects. Second, XGBoost was chosen to demonstrate the significance of various descriptors in ITR prediction. Following that, the top 20 descriptors with the highest importance scores were chosen except for fdensity, fmass, and smass, to build concise models based on XGBoost, Kernel Ridge Regression, and deep neural network algorithms. Finally, ensemble learning was used to combine all three models and predict high melting points, high ITR material systems for spacecraft, automotive, building insulation, etc. The predicted ITR of the Pb/diamond high melting point material system was consistent with the experimental value reported in the literature, while the other predicted material systems provide valuable guidelines for experimentalists and engineers searching for high melting point, high ITR material systems. Full article

Optimizing HPC systems based on performance factors and bottlenecks is essential for designing an HPC infrastructure with the best characteristics and at a reasonable cost. Such insight can only be achieved through a detailed analysis of existing HPC systems and the execution of their workloads. The “Quinde I” is the only and most powerful supercomputer in Ecuador and is currently listed third on the South America. It was built with the IBM Power 8 servers. In this work, we measured its performance using different parameters from High-Performance Computing (HPC) to compare it with theoretical values and values obtained from tests on similar models. To measure its performance, we compiled and ran different benchmarks with the specific optimization flags for Power 8 to get the maximum performance with the current configuration in the hardware installed by the vendor. The inputs of the benchmarks were varied to analyze their impact on the system performance. In addition, we compile and compare the performance of two algorithms for dense matrix multiplication SRUMMA and DGEMM. Full article

The influence of viscoelastic polymer additives on response and recovery of turbulent pipeflow over square bar roughness elements was examined using Direct Numerical Simulations at a Reynolds number of $5\times {10}^3$. Two different bar heights for the square bar roughness elements were examined, $h/D=0.05$ and $0.1$. A Finitely Extensible Non-linear Elastic-Peterlin (FENE-P) rheological model was employed for modeling viscoelastic fluid features. The rheological parameters for the simulation corresponded to a high concentration polymer of 160 ppm. Recirculation regions formed behind the bar elements by the viscoelastic fluid were shorter than those associated with Newtonian fluid, which was attributed to mixed effects of viscous and elastic forces due to the added polymers. The recovery of the mean viscoelastic flow was faster. The pressure losses on the surface of the roughness were larger compared to the Newtonian fluid, and the overall contribution to local drag was reduced due to viscoelastic effects. Full article

This paper presents a study on the design and multiobjective optimization of a bimorph-segmented linearly tapered piezoelectric harvester for low-frequency and multimode vibration energy harvesting. The procedure starts with a significant number of FEM simulations of the structure with different geometric dimensions—length, width, and tapering ratio. The datasets train the artificial neural network (ANN) that provides the fitting function to be modified and used in algorithms for optimization, aiming to achieve minimal resonant frequency and maximal generated power. Levenberg–Marquardt (LM) and scaled conjugate gradient (SCG) methods were used to train the ANN, then the goal attainment method (GAM) and genetic algorithm (GA) were used for optimization. The dominant solution resulted from optimization by the genetic algorithm integrated with the ANN fitting function obtained by the SCG training method. The optimal piezoelectric harvester is 121.3 mm long and 71.56 mm wide and has a taper ratio of 0.7682. It ensures over five times greater output power at frequencies below 200 Hz, which benefits the low frequency of the vibration spectrum. The optimized design can harness the power of higher-resonance modes for multimode applications. Full article

This article deals with the problem of designing regression models for evaluating the parameters of the operation of complex technological equipment—hydroturbine units. A promising approach to the construction of regression models based on nonparametric Nadaraya–Watson kernel estimates is considered. A known problem in applying this approach is to determine the effective values of kernel-smoothing coefficients. Kernel-smoothing factors significantly impact the accuracy of the regression model, especially under conditions of variability of noise and parameters of samples in the input space of models. This fully corresponds to the characteristics of the problem of estimating the parameters of hydraulic turbines. We propose to use the evolutionary genetic algorithm with an addition in the form of a local-search stage to adjust the smoothing coefficients. This ensures the local convergence of the tuning procedure, which is important given the high sensitivity of the quality criterion of the nonparametric model. On a set of test problems, the results were obtained showing a reduction in the modeling error by 20% and 28% for the methods of adjusting the coefficients by the standard and hybrid genetic algorithms, respectively, in comparison with the case of an arbitrary choice of the values of such coefficients. For the task of estimating the parameters of the operation of a hydroturbine unit, a number of promising approaches to constructing regression models based on artificial neural networks, multidimensional adaptive splines, and an evolutionary method of genetic programming were included in the research. The proposed nonparametric approach with a hybrid smoothing coefficient tuning scheme was found to be most effective with a reduction in modeling error of about 5% compared with the best of the alternative approaches considered in the study, which, according to the results of numerical experiments, was the method of multivariate adaptive regression splines. Full article

In this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping method, an improved control law was derived, exhibiting faster response to changes in the output tracking error while avoiding input chattering and providing robustness to uncertain model terms. Moreover, a state observer was formulated for estimating the unknown state. The main contributions with respect to closely related designs are (i) the control law, the update law and the observer equations involve no discontinuous signals; (ii) it is guaranteed that the developed controller leads to the convergence of the tracking error to a compact set whose width is user-defined, and it does not depend on upper bounds of model terms, state variables or disturbances; and (iii) the control law exhibits a fast response to changes in the tracking error, whereas the control effort can be reduced through the controller parameters. Finally, the effectiveness of the developed controller is illustrated by the simulation of concentration tracking in a stirred chemical reactor. Full article

When culturing cells in space or under altered gravity conditions on Earth to investigate the impact of gravity, their adhesion and organoid formation capabilities change. In search of a target where the alteration of gravity force could have this impact, we investigated p130cas/BCAR1 and its interactions more thoroughly, particularly as its activity is sensitive to applied forces. This protein is well characterized regarding its role in growth stimulation and adhesion processes. To better understand BCAR1′s force-dependent scaffolding of other proteins, we studied its interactions with proteins we had detected by proteome analyses of MCF-7 breast cancer and FTC-133 thyroid cancer cells, which are both sensitive to exposure to microgravity and express BCAR1. Using linked open data resources and our experiments, we collected comprehensive information to establish a semantic knowledgebase and analyzed identified proteins belonging to signaling pathways and their networks. The results show that the force-dependent phosphorylation and scaffolding of BCAR1 influence the structure, function, and degradation of intracellular proteins as well as the growth, adhesion and apoptosis of cells similarly to exposure of whole cells to altered gravity. As BCAR1 evidently plays a significant role in cell responses to gravity changes, this study reveals a clear path to future research performing phosphorylation experiments on BCAR1. Full article